Exploring Mathematics in Careers

1. Complete the warm up in the warm up section of your notebook: Think about various careers and how they use mathematics. List these on your paper. List all the possible ways they may use mathematics.

2. 2-1 Integers Course 2 Warm Up Problem of the Day Lesson Presentation

3. Warm Up Compare. Use <, >, or = 1.7 5 2. 32 65 3. 82 28 4. 64 48 > < > >

4. Problem of the Day Place 4, 5, 6, 7, 8, and 9 in the empty circles so that each side has the same sum. 1 6 9 5 7 3 4 2 8

5. Learn to compare and order integers and to determine absolute value.

6. Vocabulary opposite integer absolute value

7. The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own opposite. –4 and 4 are opposites –4 4 • • 1 2 3 4 5 –5–4–3–2–1 0 Positive integers Negative integers 0 is neither positive nor negative

8. Remember! The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . . The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet.

9. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Additional Example 1: Graphing Integers and Their Opposites on a Number Line Graph the integer -7 and its opposite on a number line. 7 units 7 units The opposite of –7 is 7.

10. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Check It Out: Example 1 Graph the integer -5 and its opposite on a number line. 5 units 5 units The opposite of –5 is 5.

11. You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

12. Remember! –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 The symbol < means “is less than,” and the symbol > means “is greater than.” Additional Example 2A: Comparing Integers Using a Number Line Compare the integers. Use < or >. 4 -4 > 4 is farther to the right than -4, so 4 > -4.

13. -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Additional Example 2B: Comparing Integers Using a Number Line Compare the integers. Use < or >. -15 -9 > -9 is farther to the right than -15, so -15 < -9.

14. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Check It Out: Example 2A Compare the integers. Use < or >. 6 -6 > 6 is farther to the right than -6, so 6 > -6.

15. -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Check It Out: Example 2B Compare the integers. Use < or >. > -4 -11 -4 is farther to the right than -11, so -4 > -11.

16. August 9, 2012 Warm Up: Place the following numbers on a number line and place them in order from smallest to largest under the number line: 0, ½ , 1, - ½ , ¾ , - ¾ , 2 , -3

17. CCGPS MCC7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MCC7.NS.1a Describe situations in which opposite quantities combine to make 0. MCC7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real‐world contexts.

18. Essential Question: Can you arrange numbers from least to greatest using a number line and add integers using a zero pair?

19. –8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 Additional Example 3: Ordering Integers Using a Number Line. Use a number line to order the integers from least to greatest. –3, 6, –5, 2, 0, –8 The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

20. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Check It Out: Example 3 Use a number line to order the integers from least to greatest. –5, 4, –3, 2, –1, –2 The numbers in order from least to greatest are –5, –3, –2, –1, 2, and 4.

21. absolute value – the distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero.

22. 8 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Additional Example 4A: Finding Absolute Value Use a number line to find each absolute value. |8| 8 is 8 units from 0, so |8| = 8.

23. Reading Math The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.

24. 12 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Additional Example 4B: Finding Absolute Value Use a number line to find each absolute value. |–12| –12 is 12 units from 0, so |–12| = 12.

25. 3 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Check It Out: Example 4A Use a number line to find each absolute value. |3| 3 is 3 units from 0, so |3| = 3.

26. 9 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Check It Out: Example 4B Use a number line to find the absolute value. |–9| –9 is 9 units from 0, so |–9| = 9.

27. • • • • • –5–4 –3 –2–1 0 1 2 3 4 5 Lesson Quiz: Part I Compare. Use <, >, or =. 1. –32 32 2. 26 |–26| 3. –8 –12 4. Use a number line to order the integers –2, 3, –4, 5, and –1 from least to greatest. < = > –4, –2, –1, 3, 5

28. 3 units –5 –4 –3 –2 –1 0 1 2 3 4 5 Lesson Quiz: Part II Use a number line to find the absolute value. 5. -3 • 3

29. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Plot the following on a number line & list them from smallest to largest : 6, 2, -3, 0, -5, 1

30. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Plot the following on a number line & list them from smallest to largest : ½, 2, -3, 0, -5, 1½ , -1 ½, -6

31. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Plot the following on a number line & list them from smallest to largest -8, 4, -6, 1, 0, -2, 7, -2½

32. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Plot the following on a number line & list them from smallest to largest -1, -3, 2, 5, -5, 7, 0

33. Integer Chips